New Automotive Air Conditioning System Simulation Tool Developed

INTRODUCTIONWhen operated, the air-conditioning (A/C) system is the

largest auxiliary load on a vehicle. A/C loads account formore than 5% of the fuel used annually for light-dutyvehicles in the United States [1]. A/C loads can significantlyimpact electric vehicle (EV), plug-in hybrid electric vehicle(PHEV), and hybrid electric vehicle (HEV) performance.Mitsubishi reports that the range of the i-MiEV can bereduced by as much as 50% on the Japan 10-15 cycle whenthe A/C is operating [2]. The advanced powertrain researchfacility at Argonne National Laboratory has reported a nearly20% reduction in range in the Nissan Leaf operating on theUDDS cycle. A hybrid vehicle tested at NREL showed 22%lower fuel economy with the A/C on [3]. Increased coolingdemands from the battery thermal management system in anEV may impact the A/C system. Heavy-duty vehicles alsoneed a tool to evaluate the impact of A/C on both “down-the-

road” and idle conditions. Cabin climate conditioning is oneof the primary reasons for operating the main engine in along-haul truck during driver rest periods. In the UnitedStates, long-haul trucks (trucks that travel more than 500miles per day) use 838 million gallons of fuel annually forrest period idling [4]. A flexible open-source analysis tool isneeded to assess the A/C system's impact on advancedvehicles. The industry has expressed a need for both astandalone A/C system model as well as an A/C model thatcan co-simulate with a vehicle simulator such as Autonomie[5]. This model expands the capability of vehicle simulationtools, including Autonomie, and addresses industry needs.

The A/C system contains complex flow, thermodynamics,and heat transfer. On the refrigerant side, the flow is transientand both compressible and two-phase. Calculating refrigerantproperties near the phase transitions can also becomputationally difficult. Air flow through the condenser canvary widely depending on vehicle speed and condenser fan

2013-01-0850Published 04/08/2013

doi:10.4271/2013-01-0850saepcmech.saejournals.org

A New Automotive Air Conditioning System Simulation ToolDeveloped in MATLAB/Simulink

Tibor Kiss and Lawrence ChaneyNational Renewable Energy Laboratory

John MeyerVisteon Corporation

ABSTRACTAccurate evaluation of vehicles' transient total power requirement helps achieving further improvements in vehicle fuel

efficiency. When operated, the air-conditioning (A/C) system is the largest auxiliary load on a vehicle, therefore accurateevaluation of the load it places on the vehicle's engine and/or energy storage system is especially important. Vehiclesimulation models, such as “Autonomie”, have been used by OEMs to evaluate vehicles' energy performance. However,the load from the A/C system on the engine or on the energy storage system has not always been modeled in sufficientdetail. A transient A/C simulation tool incorporated into vehicle simulation models would also provide a tool fordeveloping more efficient A/C systems through a thorough consideration of the transient A/C system performance. Thedynamic system simulation software MATLAB/Simulink® is frequently used by vehicle controls engineers to developnew and more efficient vehicle energy system controls. A MATLAB/Simulink-based transient A/C system simulationmodel is easier to incorporate into MATLAB/Simulink-based vehicle simulation software; therefore, the availability of atransient A/C system simulation tool developed in the MATLAB/Simulink platform is important.

NREL has recently developed an A/C simulation tool to address these needs. This paper describes in detail themodeling methods used for this new simulation tool. Comparison with measured data is provided to demonstrate thevalidity of the model. The agreement between simulation and measurement was shown to be good on both the componentand system level. The capabilities of the model are also demonstrated by the example of simulating the SC03 cycle.

CITATION: Kiss, T., Chaney, L. and Meyer, J., "A New Automotive Air Conditioning System Simulation Tool Developedin MATLAB/Simulink," SAE Int. J. Passeng. Cars - Mech. Syst. 6(2):2013, doi:10.4271/2013-01-0850.

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NREL/CP-5400-57488. Posted with permission. Presented at the SAE 2013 World Congress and Exhibition

speed. The heat transfer in the heat exchangers is a verycomplex process mainly addressed by complex correlationsbased on measured data. These correlations sometimes reducethe stability of the code. The effects of humidity are difficultto account for, not only in the model but also for theexperimental data necessary to calibrate the code. A cabinmodel is also needed to provide a realistic load on theevaporator. The cabin model must consider all the majorpathways of heat transfer into the cabin, including solar andconvective loads from the environment, heat from the enginecompartment, and sensible and latent heat loads in the airstream. Realistic control methods similar to ones actuallyused in automotive A/C systems also have to beimplemented. The cycling of the compressor can introducequick transients that are sometimes difficult to handle by thenumerical solver. The simulation model also has to be fastenough for the purpose of evaluating vehicle powerperformance and/or the design of A/C systems and theircontrols.

There are numerous challenges in developing a suitableautomotive A/C system simulation tool. Some examples ofpreviously developed non-commercial full system-levelsimulation include [6,7,8]. However, to the best of ourknowledge, none of them is both developed in the widelyused dynamic system simulation platform MATLAB/Simulink (which is helpful for controls engineers) andavailable to the public at the same time. Commerciallyavailable software tends to be very expensive, and typically,their accuracy for predicting the transient processes isdifficult to assess based on available documentation. Thesimulation model subject of this paper addresses these issues.Also, with the model being built on the MATLAB/Simulinkplatform, most of the inner workings of the model are visibleto the user, and the user has considerable freedom to modifythe model to better represent their specific A/C systemhardware and controls. Only the source codes for some of thebasic building blocks of the model remain inaccessible to theuser.

SELECTING THE MODELINGMETHOD

Numerically, the most difficult part is modeling the two-phase refrigerant flow circuit. A number of different methodshave been used in the past, and the selection of which methodto use was based on the intended purpose of the simulationmodel.

With the transient nature of automotive A/C systems, theauthors thought it was most important that the modelingmethod capture the transient processes accurately androbustly, even if model execution speed was compromised.The model should be robust for fast transients such ascompressor cycling. It should also accurately predictrefrigerant redistribution after shut-down and after start-up. Ithas to conserve mass accurately during simulations of longtest cycles.

Another desirable feature of the model was that it shouldbe versatile enough that various complex heat transfercorrelations can be programmed into the main algorithmrelatively easily. Finally, the model formulation had to be onethat was well suited for the simulation modeling platform,MATLAB/Simulink.

The authors decided to use the finite volume formulationfor calculating the refrigerant flow. The finite volumeformulation is well suited for accurate conservation of massmomentum and energy. Also, in the finite volumeformulation, immediately after each step of the integrator, thestate variables and the velocity are readily available. Then,heat transfer rates even with the more complex methods canbe calculated explicitly. Finally, Simulink is geared towardsolving ordinary differential equation systems and, in thefinite volume formulation, the problem is established as a setof ordinary differential equations. Therefore, this formulationis very well suited for Simulink.

Challenges were expected with the “stiff” nature of thismodeling method, especially in the condenser where pureliquid is present.

DESCRIPTION OF THE MODELThe transient A/C simulation model consists of two main

sub-models that include the cooling circuit model and thecabin model. In the cooling circuit model, the larger volumescontaining refrigerant, such as the accumulator, the receiver/dryer, and the headers of the heat exchangers, are modeledwith the zero-dimensional volume simulation block (0-Dvolume block). The refrigerant pipes and the flat tubes /plates of the heat exchangers are modeled with variousversions of the one-dimensional pipe simulation block (1-Dpipe block). The general structure of the model on therefrigerant side is a network of 1-D pipe blocks connected toeach other with 0-D volume blocks.

Using the 0-D volume and the 1-D pipe blocks, models ofvarious multi-pass multi-row compact heat exchangers can becreated relatively easily. Models for other A/C systemcomponents, such as the compressor and the thermostaticexpansion valve, were incorporated with the goal ofmaintaining sufficient accuracy and acceptable executionspeed. The model currently uses R134a exclusively as therefrigerant. However, other refrigerants can be used if theuser builds the required property tables in a specified text fileformat.

In the following sections, the 0-D volume block, the 1-Dpipe block and various other modeling blocks are describedin detail.

The 0-D Volume Simulation BlockThe 0-D volume blocks serve as models for real volumes

in the system as well as the connectors between the 1-D pipeblocks. In the 0-D volume block, the sum of the incomingrefrigerant mass flow rates minus the sum of the outgoingrefrigerant mass flow rates determine the time derivative of

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the refrigerant mass in the volume, and the sum of theincoming refrigerant enthalpy flow rates minus the sum of theoutgoing refrigerant enthalpy flow rates plus the net heattransfer to the volume determine the time derivative of theinternal energy in the volume. Note that when saturatedconditions exist in the 0-D volume block, saturated liquid,saturated vapor, or a saturated mix can be selected for theoutput flow, according to the system component representedby the simulation block. An accumulator, for example, isphysically designed to only let out saturated vapor.

Since internal energy and mass are the state variables forthe simulation, all other material properties are looked upfrom two-dimensional tables based on specific internalenergy and density. Such lookup tables provide the bestnumerical performance as no iteration on properties isrequired.

The 1-D Pipe Simulation BlockIn all versions of the 1-D pipe simulation blocks, on the

refrigerant side, equations for conservation of mass,momentum and energy are solved through a finite volumemethod. As with the 0-D volume block, all refrigerantmaterial properties are obtained from two-dimensional tablesbased on specific internal energy and density. The evaluationof heat transfer between the pipe wall and the refrigerant, andbetween the pipe wall and air is incorporated through localheat transfer coefficient correlations. The effectiveness-NTUmethod is applied on the air side, which ensures that the exitair temperature does not overshoot the wall temperature. Thetime derivative of the wall temperature is calculated from thenet heat flow rate to the wall. Therefore, the thermal capacityof the wall has been accounted for. However, the temperaturedrop across the pipe wall has not been accounted for. It wasdetermined that the introduced error is small for the relativelythin walls of the flat tubes / plates found in typical compactheat exchangers in an A/C system. In the direction of airflow, the temperature of the wall is constant. From theapplied finite volume method, it is inherent that in the 1-Dpipe simulation block, refrigerant flow can take place in bothdirections.

The simplest version of the 1-D pipe simulation block isused to model the refrigerant lines connecting the variousA/C system components. Here a circular pipe is simulated ina perpendicular cross-flow of air. For these connecting lines,the effects of the relative humidity and condensation of wateron the pipe are neglected.

More complex versions of the 1-D pipe simulation blockare used for simulating the refrigerant and air flow and heatexchange process for the flat tubes of the condenser andplates of the evaporator. These 1-D pipe model blockversions include the options of multiple “parallel channels”on the refrigerant side and more complex fin geometry on theexternal air flow side. Humidity in the air and condensationof water from air is accounted for. It is assumed that therefrigerant flow properties inside the parallel channels areidentical. Also, the wall/fin temperatures in the direction of

the air flow are assumed to be constant. This is certainly anapproximation, but one necessary to maintain reasonablesimulation execution speed.

The finite volume formulation that is used for therefrigerant flow is a conservative method in the sense that themass, momentum and energy are conserved very accurately.For the air flow, there are no conservative terms and the flowis described with purely algebraic equations.

Refrigerant-side equationsThe general control volume equations for the conservation

of mass, momentum and energy as presented in [9] are usedas a starting point. The general control volume equations arethen written for one dimension, as all flow variables areassumed to change only in the direction of refrigerant flow,and for finite volumes, that is small volumes, over which theflow variables can be considered uniform. Note that therefrigerant is in thermodynamic equilibrium in the finitevolumes, and velocity “slip” between the liquid and the vaporphase is not factored in. The refrigerant is also consideredhomogeneous, that is, all flow properties, including liquidand vapor phase volume ratios, are the same everywherewithin the finite volume. Finally, the effects of gravity areneglected.

Conservation of massWe start out from the conservation of mass ([9], Eq.

3.3.1):

(1)

where ρ is the refrigerant density, is the velocity vector, ∫cv

dV is the volume integral and is the surface integral.The first integral on the right is the mass in the finite volume,and then for the one dimensional flow for the finite volume:

(2)

where A is the pipe cross sectional area, and the in / outsubscripts are for inlet and outlet boundaries of the finitevolume, defined also as the left-side and right-sideboundaries, respectively, as we use the convention that thepositive flow is from left to right.

Conservation of momentumThe conservation of momentum written for a control

volume ([9], Eq.3.3.8):

(3)

where ΣF is the sum of all forces including shear andpressure forces on the control volume. We define the firstintegral on the right side as the linear momentum, I. For finite

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volume formulation for one-dimensional flow the followingcan be written:

(4)where pin and pout are the pressures on the inlet and outletboundary, respectively, and Fwf is the force from wallfriction. For the wall friction force, a version of the Darcy-Weisbach formula ([9], Eq.5.8.7) was used in which the wallfriction factor was obtained with the Hagen-Poisseuilleequation ([9], Eq. 5.10.12) for laminar flow and from amodified version of the Colebrook equation ([9], Eq. 5.10.13)for turbulent flow. This latter equation does take into accountthe effect of the relative roughness of the pipe wall. Theseequations are used for both single and two-phase flow. In thetwo-phase region, the viscosity was obtained as the qualityweighted average of the saturated liquid and saturated vaporviscosity. A user-adjustable calibration coefficient was alsoimplemented.

Conservation of energyThe energy equation written for a control volume ([9], Eq.

3.3.6):

(5)

where is the rate of heat addition, is the rate of workdone by the system via shear forces, and e is the total energy

per unit mass: , where u is the specific internalenergy and ν is the velocity. Note that all components otherthan the internal and kinetic energy have been neglected. Thisequation also assumes no other boundary work than that onthe inflow and outflow surfaces. We define E as the firstintegral on the right side, which is the total energy in thefinite volume. Then, assuming 1-D flow, no shear force work,and heat addition strictly through the pipe wall (noconductive heat transfer through inflow/outflow boundaries),the following equation can be written for each control volumein the pipe (also will be called as a “segment” of the pipe):

(6)where Qwr is the heat transfer rate from the pipe wall to therefrigerant flowing inside the pipe segment. Note that Qwrcan be written as

(7)

where is the average heat transfer coefficient over the pipesegment, Ai is the inside area of the pipe segment wall, andTw is the pipe segment average wall temperature. To calculate

, the Dittus-Boelter equation ([10], Eq. 8.58) and/or theChen correlation [11] is used. Note that the transition pointsbetween the single-phase and two-phase regions along thelength of the pipe need to be determined for the properapplication of the heat transfer rate correlations. Thesetransition points are easily obtained from the mass and totalenergy, which are simulation state variables and thereforeavailable in the finite volumes at the start of each time step.

Spatial discretizationThe spatial discretization was implemented as shown in

Fig. 1. Note that a “staggered” grid was used. While thecontrol volumes were defined for mass and energy as thevolumes shown between the 0-1, 1-2, 2-3, … location indexes(Type 1 finite volumes), for the linear momentum they weredefined as the volumes between the 0-0a, 0a-1a, 1a-2a, 2a-3a,… location indexes (Type 2 finite volumes). So in fact thereare two sets of finite volumes, one set for the mass andenergy equations, and one set for the momentum equations.This staggered spatial discretization method had to be used toavoid instability problems. Other authors have also used thismethod [12], perhaps for the same reason. Note that the firstand last Type 2 finite volumes (finite volumes for linearmomentum) are “half” size compared to the rest of the onesin the middle of the pipe.

Fig. 1. Spatial resolution for the finite volumeformulation

To implement the conservation equations, the variablesρin, ρout, pin, pout, νin, νout, uin and uout (the density, pressure,velocity and specific internal energy on the finite volumeboundaries, respectively) have to be obtained from theconserved variables m, I and E (the mass, the momentum andenergy, in the finite volumes, respectively). The conservedvariables are also the simulation state variables that areavailable immediately after the integrator advances one timestep. From the definition of these variables:

(8)

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(9)

(10)

(11)

Then a simple first-order interpolation of the flowvariables on the finite volume boundaries was implemented.For example, for the conservation of mass, the density andvelocity on the left-side boundary of the ith Type 1 finitevolume is estimated as

(12)

(13)

and for the conservation of momentum equation, the densityand velocity on the left-side boundary of the ith Type 2 finiteboundary are estimated as

(14)

(15)

Note how the interpolations are different betweenconservation of mass and conservation of linear momentumdue to the staggered Type 1 and Type 2 finite volumes.

Applying the boundary conditionsIn this section we discuss the boundary conditions of the

overall computational domain, that is, the left-side boundaryof the first finite volume and the right-side boundary of thelast finite volume. Flow variables on these surfaces cannot becalculated the same way as on the boundaries between twofinite volumes because they are attached to 0-D volumeblocks. The boundary conditions have to be treateddifferently depending on whether inflow or outflow waspresent on the boundary, determined by the sign of the linearmomentum, I. For the inflow, conditions from the connected0-D volume block could be applied readily to obtain theboundary conditions. Calculating the outflow boundaryconditions is more challenging as there are various ways ofextrapolating flow variables to the boundary and some ofthese methods did not work well regarding stability, accuracyor speed. In the end, the following method was found to workwell. To calculate the boundary velocity, the linearmomentum in the Type 2 boundary finite volume (availableas state variable) was divided by one-half the mass in theType 1 boundary finite volume. The boundary pressure foroutflow was simply the pressure in the connected 0-Dvolume. The specific internal energy on the boundary wasextrapolated linearly from the first two regular Type 1 finite

volumes next to the boundary. Finally, once the boundaryinternal energy and pressure were known, the boundarydensity could be calculated through an iterative process usingthe pressure vs. specific internal energy and density tables.

Air-side equationsThe heat transfer rate from the air flow to the wall of a

pipe segment can be written as

(16)

where is the average air-to-wall heat transfer coefficient inthe pipe segment, Tw is the pipe segment average walltemperature, and Atot is the total surface available for heattransfer on the air side in the pipe segment.

The air-side equations are different for the variousversions of the 1-D pipe model blocks. For the transportrefrigerant pipes, the correlation for heat transfer on a pipe ina perpendicular cross-flow of air was implemented accordingto Eq. 7.53 of [10]. For air-side heat exchange on the finnedheat exchangers, the Chang correlation [13] wasimplemented. It is noted that although the Chang correlationdid not incorporate the effects of humidity and condensation,we still apply this correlation for moist air.

Chang proposed a detailed and a simplified correlation,where the local heat transfer coefficient is calculated by usinga correlation for the Colburn j-factor, j. The simplifiedcorrelation is

(17)

where ReLp is the Reynolds number based on the louverpitch, Lp (see Fig. 2). The more complex version of theChang correlation incorporates a dependency on louver angle,fin length, tube depth, louver length, tube pitch and finthickness. The model user can switch between the simplifiedand more detailed correlation versions. The details of how theheat transfer coefficient can be obtained from the Colburn j-factor can be found in [10] p.534.

Fig. 2. Louver pitch used in the Chang correlation

The local heat transfer coefficient, ha obtained by eitherthe simpler or the more complex Chang correlation has to be

adjusted to get an average heat transfer coefficient, byincorporating the effects of the fins not being able to maintainthe same temperature as the flat tube itself

(18)

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where η0 is the fin effectiveness, which can be written as

(19)Here Atot is the total area for heat transfer, Af is the finned

area available for heat transfer and ηf is the fin efficiency.The fin efficiency for the straight fins between two flattubes / plates can be expressed as ([10], Eq.11.4):

(20)where L is the half fin length, m = (2h/kt), k is the thermalconductivity of the fin material, and t is the fin materialthickness.

With that, the equation (16) can be evaluated, but it willbe accurate only as long as the temperature change of the airacross the flat tube is small relative to the difference betweenthe incoming air temperature and the flat tube walltemperature. In general that cannot be assumed and thereforethe effectiveness-NTU method is used as applied to a parallelflow heat exchanger ([10], Eq.11.29a):

(21)where Cr is the ratio of the lower and the higher heat capacityrates:

(22)where the heat capacity rate is the mass flow rate of themedium participating in the heat transfer times its constantpressure specific heat. Because the wall temperature isconstant, the refrigerant side can be represented by infinitelylarge heat capacity flow and heat transfer rate that ensuresconstant metal temperature along the air flow direction.Therefore, in our special case Cr approaches zero, and theabove equation simplifies to

(23)Furthermore, assume that the heat transfer takes place

from the air to the flat tube / plate wall. Then

(24)can be written ([10], Eq. 11.26), where the subscripts a, w, iand o mean air, wall, in and out, respectively. Finally, per[10], Eq. 11.25,

(25)

where is the air mass flow rate and Cp,a is the constantpressure specific heat for the incoming “wet” air, and after U

was replaced with justified by an infinitely large heatcapacity flow rate assumed on the refrigerant side. Also, itcan be easily shown that

(26)

where Cp,adry and Cp,w are the constant pressure specificheats for dry air, and water vapor, respectively, and ω is theabsolute humidity. Then, from the above three equations, Ta,ocan be expressed as

(27)

The air-to-wall heat transfer rate now can be obtained as

(28)

where is the mass flow rate of the water vapor carried bythe wet air. The result would be the same if we had assumedthe heat transfer to take place from the flat tube to the air.

At this point the issue of condensation needs to beaddressed. Water vapor condensation in the air flowingthrough the evaporator has a significant effect on thetemperature and relative humidity of the wet air leaving theevaporator; therefore, it needs to be accounted for. In thecondenser, there is no water condensation, but the relativehumidity still has some effect on the results. The same air-side model is used for both evaporator and condenser. Whenused for the condenser or for an evaporator seeing lowhumidity incoming air, the majority of condensation-relatedcalculations do not get executed; therefore, the performancepenalty is insignificant compared to using a dedicated non-condensation pipe model.

Mass flow rate, temperature, and the relative humidity ofthe incoming wet air for each pipe segment are inputvariables. The air flow velocity is calculated using theminimum area for air flow inside the heat exchanger, whichis an input parameter.

The air-side heat transfer equations are solved for eachsegment of the pipe. First, the heat transfer rate is calculatedas it would be without condensation. The wet air enthalpy isreduced using the heat transfer rate and an air-outtemperature is calculated. The partial pressure of the watervapor in the exit wet air is calculated with the exit pressure,exit temperature and the incoming relative humidity. Thesaturated water vapor pressure is also calculated for the exitair temperature. If the saturated water vapor pressure ishigher than the exit air water vapor partial pressure, then

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there is no condensation. In this case all previously calculatedproperties will be valid, and the calculation can proceed tothe next pipe segment. If the saturated water vapor pressure islower than the exit air water vapor partial pressure,condensation of water does take place, and the flowproperties have to be recalculated for the pipe segmentconsidering condensation. The algorithm for condensationconditions assumes that the exiting atmospheric air issaturated with water vapor, and this exit air-vapor mix is atthe same temperature as the condensed water. The algorithmthen invokes an iteration on the exit wet air temperature,while the heat transfer to the heat exchanger wall is stillassumed to be the same as it would be without condensation.It is not known to the authors how much error thisassumption introduces. Other treatment of condensationwould involve much more complicated heat transferequations that incorporate the presence of a liquid water layerover the heat exchanger surfaces.

Once the exit wet air temperature is obtained, all other airflow properties can easily be calculated for the current pipesegment. Next, the same process will be applied to all theremaining pipe segments.

Parallel channelsIn order to model a typical condenser configuration,

multiple “parallel” channels for refrigerant flow are allowedin a 1-D pipe block. These channels are identical in terms ofrefrigerant flow. Because the wall temperature is assumedconstant within a pipe segment, the wall-to-refrigerant heattransfer rate is also identical in the parallel channels.Therefore, the refrigerant in and out mass flow rates and thewall-to-refrigerant heat transfer rates for a single parallelchannel are simply multiplied by the number of parallelchannels in the flat tube to get the aggregate numbers for theentire flat tube.

Coupling the air and refrigerant sidesThe air and refrigerant-side equations can be solved on

their own separately, because the two sets of equations arenot algebraically coupled. The pipe wall temperature, Tw,appears in both sets of equations, but it is a simulation statevariable, which means its value is obtained as a result of anintegration step, not from algebraic equations. Therefore, it isavailable at the beginning of each time step to calculate theheat transfer rates from the air to the pipe wall and from thepipe wall to the refrigerant.

It is assumed that the thermal resistance of the wall iszero. In other words, the inner and outer surfaces of the pipewall are at the same temperature. This is typically a goodapproximation for compact heat exchangers as they use thinwalls.

The equation for the wall temperature comes from theconservation of energy, which states that the net heat fluxinto the wall segment is stored as thermal energy in the wallsegment:

(29)

where Qaw is the heat transfer rate from air to the wall, Qwr isthe heat transfer rate from the wall to the refrigerant, Qx is theheat transfer rate in the pipe wall in the refrigerant flowdirection, Cpw is the wall material specific heat, and Δm is the

mass of the wall segment including all the fins. The term represents the imbalance in conductive heat flow ratesfrom the neighboring wall segments. This equation is writtenfor each pipe segment, and the wall temperature is obtainedfor each pipe segment.

Heat ExchangersCurrently, the typical heat exchangers in automotive A/C

systems are compact heat exchangers with a general structurethat can be described as a number of headers, with “passes”between these headers. Nearly all of the heat transfer takesplace in the passes. Using conventional terminology, one passin the condenser consists of a number of flat tubes and onepass in the evaporator consists of a number of plates.

Two versions of the above described 1-D pipe modelsimulation block, with air-side heat transfer according to theChang's model, are the basic building block for the heatexchangers in the A/C system model. For the version used tomodel the flat tubes of the condenser, the Dittus-Boelterequation is used on the refrigerant side along the full lengthof the pass, even across the phase boundaries. In the saturatedmix region, quality weighted average of the saturated liquidand saturated vapor properties of the refrigerant are used.This simple model provided a good match with measurement.For the version used to model the plates of the evaporator, onthe refrigerant side, the Dittus-Boelter equation [10] is usedfor the superheat region and the Chen correlation [11] is usedfor the two-phase region.

In the following paragraphs we use the example of anevaporator; therefore, we will use the term “plates” but thesame could be said about the condenser, using the “flat tubes”terminology. With the help of the 0-D volume and 1-D pipesimulation blocks, multiple row and multiple pass heatexchangers can be built relatively easily. The simplestapproach is to have one 0-D volume block for each of theheaders and connect them with one 1-D pipe model block,each representing one pass. In order to account for thenumber of plates in each pass, the mass flow rate and heattransfer outputs have to be multiplied by the number of platesin the pass before being routed into the 0-D volume blocksrepresenting the headers. Therefore, in this approach all theplates in a given pass are treated as identical in terms of theirflow and heat transfer. A sub-version of this approach iswhen the plates in a pass are split up into “sub-passes”depending on which pass is upstream of them in terms ofairflow. Each of these sub-passes is then represented with oneplate model, and mass flow and heat transfer through a sub-

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pass are once again obtained by mass flow and heat transferthrough one plate multiplied by the number of plates in thesub-pass. An example of how this works is shown in Figs. 3aand 3b for the case of a two-row, two-passes-per-rowevaporator for which one of the passes, pass 2, gets theairflow from two different upstream passes. As explainedabove, this pass is then split up into pass 2a and pass 2b,which receive their air flow from passes 3 and 4, respectively.This is the configuration of the evaporator in the currentmodel implementation.

Fig. 3a. Schematic of the implemented evaporatorshowing air flow dependency of passes

Fig. 3b. The “exploded view” schematic of theimplemented evaporator showing the headers

A more rigorous way to build a compact heat exchangermodel would be to represent each plate with a dedicated 1-Dpipe simulation block. Accuracy would be expected toincrease, but the much increased simulation execution timereduces the practicality of this approach.

Routing the airflow is also relatively easy with the appliedmodeling methodology. The segment-wise exit air flowvariables from a plate are passed as an output vector from the1-D pipe simulation block representing the plate. This vectorcan be directly fed into the inlet air flow variables input portof the simulation block representing another plate in anotherdownstream row/pass. For some cases this is done with adirect connection, for example, when the plates in theupstream row and in the downstream row are aligned and the

refrigerant flow direction is the same in them (see pass 3 airexit flow to pass 1 air inlet flow). In other cases, the order ofthe passed air flow variables vector needs to be reversed (seepass 3 air exit flow to pass 2a air inlet flow).

Alternatively, the exit air flow output vector can be fedthrough another simulation block, the “mixing” block thatcalculates the flow properties of the mixed out stream. Thisoption can be used for the last row of the heat exchangerswhere the airflow from the plate is also exiting the whole heatexchanger. The variables of the mixed out-flow are calculatedfrom the variables of the individual pipe segment exit flowsbased on the conservation of mass and energy. Additionalcondensation may take place during the mixing, and it isaccounted for in the calculation. The mixing block can alsobe used when the plates do not obviously align or differentnumbers of pipe segments are desired to be used in thedifferent passes due to numerical stability considerations.

Thermostatic Expansion ValveThe expansion device implemented in the model is an

externally balanced thermostatic expansion valve (TXV).Delayed response of the bulb temperature to changes in theevaporator exit temperature is achieved with a first-orderdelay simulation block. The characteristic time of thisresponse is an input parameter to the model. The bulbpressure is the saturated pressure of the refrigerant at the bulbtemperature.

This response is the only dynamically modeled detail.Otherwise, the position of the valve ball is determined fromstatic force balance. The moving masses inside the TXV areso small that the characteristic time of the valve ball positionresponse to changing pressures is very small. Some wavephenomenon may make a difference here; however, themodel would not be very efficient if such detail is included -the simulation time step would have to be very small. Theinput parameters that play into the TXV static force balancecalculation include the spring preload, the spring rate, the balldiameter, ball seat angle, actuating pin diameter, and the bulbactuator diameter. Furthermore, the ball stroke limits themaximum opening area and can be adjusted for a given tonrating of the TXV.

Once the flow area through the flow restriction device ofthe valve is known, the refrigerant flow rate is calculatedfrom the two-phase orifice flow equations. In addition to theflow area, the upstream conditions and the downstreampressure are used in this calculation. First the modeldetermines the critical pressure, p*, and critical unit areamass flow rate, q*, from lookup tables, based on upstreampressure, pu, and enthalpy, hu:

(30)

(31)These lookup tables were generated for R134a from other

property tables with the conditions that the flow is isentropic

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between the inlet and the throat, and that the Mach numberequals one in the throat for choked flow. Then the calculationof the mass flow rate, q, depends on whether the downstreampressure, pd, is lower or higher than the critical pressure. If pd≤ p* (choked flow), the mass flow rate, q, is

(32)

where Ax is the flow area in the throat and Cd is the dischargecoefficient. On the other hand, if pd > p* (non-choked flow),the mass flow rate is calculated from the conditions that theflow is isentropic between the inlet and the throat, and thatthe enthalpy in the throat is the enthalpy at the inlet minus theflow kinetic energy at the throat (the steady state flow versionof the energy equation with zero inlet kinetic energyassumption).

The equations implemented in the orifice model are validfor adiabatic one-dimensional homogeneous equilibrium two-phase flow. However, adjustment was made to approximatesome non-equilibrium effect. Data measured for short orificeswas used for this purpose [14]. A discharge coefficient wasdetermined as the ratio of the actual mass flow rate to themass flow rate predicted by the above equilibrium calculationmethod. It was noticed that the discharge coefficient was afunction of how far the upstream conditions deviated fromsaturated liquid conditions. Therefore, the dischargecoefficient can be set as a function of pr, the ratio of theupstream pressure and the saturated liquid pressure atupstream enthalpy:

(33)

The success of this approach is demonstrated in Fig. 4a inwhich 40 short-orifice R134a flow data points with variousupstream conditions and downstream pressures were plottedon the p-h space, and the calculated discharge coefficients foreach data point were plotted as a function of the variable pr inFig. 4b. The correlation fit line that was developed andimplemented in the model is shown in Fig. 4b. The orifice forthis correlation was 1.22 mm in diameter and 13.1 mm long,and arguably quite different in shape from the inner details ofthe flow path in a TXV. However, there is a reasonablefreedom built into the input parameter list of the TXVsimulation block to adjust the shape of the Cd(pr) curve forTXV data that the user may have available.

Note that with proper selection of input parameter values,the TXV model can easily be reduced to an orifice tubemodel. No modification to the Simulink model is needed forthis purpose.

Fig. 4a. Short-orifice data points on p-H space

Fig. 4b. Calculated Cd plotted against the variable Pr

CompressorThe compressor is a constant volume variable speed

displacement device. The rotational speed and thedisplacement per revolution (both input parameters)determine the ideal forwarded volume per second. Actualforwarded volume per second is then obtained with theapplication of a volumetric efficiency. Upstream conditionsand downstream pressure are input. The downstream enthalpyis calculated with the help of an isentropic efficiency ([15],Eq. 6-62).

Both the volumetric and the isentropic efficiencies arefunctions of the compressor speed and the downstream-to-upstream pressure ratios. These tables are input to the model.There are two versions of the model, one for a mechanicaland one for an electric drive compressor. The compressorefficiency tables are different for these model versions. Forthe mechanical drive compressor version, efficiency tablestypical of a piston compressor were used. For the electric

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drive compressor version, efficiency tables typical of a scrollcompressor were used.

Compressor cycling is accounted for, and there are certaincontrols implemented for that in the model (see Controls).These controls are different for mechanical and electric drivecompressors.

Variable displacement compressors are gaining ground inmechanical drive A/C systems as they have an additionaldegree of freedom in setting the refrigerant mass flow ratecompared with a constant displacement device. Thisadditional control reduces the need for the inefficient cyclingof the compressor. It is easy for the model user to modify thiscompressor model to represent a variable displacementdevice. At this time, the effects of lubricating oil on thecompressor - or the system as a whole - have not beenaccounted for.

Cabin ModelThe cooling system model is enhanced with a cabin

model. The purpose of the cabin model is to provide areasonably accurate estimate of the cabin conditions that canserve as the boundary conditions for the cooling circuitmodel. The cabin air is represented with a zero-dimensionallump-sum air / water vapor mix volume. The cabin shell andinterior thermal masses are included. Heat transfer betweenthe thermal masses, the cabin air, and the ambient areaccounted for, as well as the solar energy absorption by eachthermal mass. The thermal masses and the heat transfer pathsthat are included in the model are shown in Fig. 5.

Fig. 5. Schematic of the cabin model

The thermal masses are shown in the rounded boxes, andthe heat transfer paths are shown with solid arrows. All bodyair leak flow rates are lumped together and calculated as anadjustable constant times the pressure differential betweenthe cabin and the ambient. The cabin model schematic isshown with the air passages for fresh and recirculated air.

ControlsBasic electronic controls have been implemented in the

model. Shut-off of the compressor due to downstreampressure passing above a high pressure limit, or upstream

pressure passing below a low pressure limit is included.Limits on how long the compressor has to stay off after eachshut-down is also implemented. The cabin air recirculationrate is set based on whether the cabin temperature exceeds theoutside temperature or not. Alternatively, the recirculationrate can be set constant over the entire simulation. Thesebasic controls are implemented for both the mechanical andthe electric drive compressor versions of the model.

In addition, for the model version with the mechanicaldrive compressor, the compressor is cycled on or offdepending on whether the cabin temperature is below orabove the target temperature and whether the evaporator-outair temperature is below or above a set target temperature (toprevent freezing). A temperature dead band is alsoimplemented for both to reduce the frequency at which thecycling occurs. The evaporator blower speed is set to one of anumber of settings at the beginning of the simulation andremains constant throughout the simulation.

On the other hand, in the model version with the electricdrive compressor, where the compressor speed can becontrolled independently of the vehicle's engine speed, thecompressor speed is adjusted based on whether theevaporator wall temperature is above or below a set target ina region just upstream of where superheat is expected in theevaporator. This way, freezing of the evaporator can beavoided most of the time without having to cycle thecompressor on and off. Unlike in the model with themechanical drive compressor, the blower flow is adjustedbased on the cabin temperature relative to the set cabin targettemperature. There is an additional compressor cyclingalgorithm: if the controller would otherwise commandbringing down the compressor RPM below a minimum, thecompressor will cycle off. When the compressor restarts, itrestarts at that same minimum RPM. This is done so that thecompressor does not operate in the inefficient low RPMregime.

These controls are easily modified and additional controlalgorithms can be added by the user given the blocksimulation environment of Simulink. In fact, one of the bestapplications of this model may be the development of controlsystems for optimum A/C system performance andefficiency. The fact that the model handles compressor shut-down and start-up transients robustly and at least in theoryaccurately, is an important feature of the model in this regard.

Model PerformanceDuring development, it was an important goal that the

model would run at an execution speed that is practical forthe development of A/C systems and in the evaluation ofvehicle power management, for example, when used in co-simulation with Autonomie. The execution speed isdominated by the small time step required by the model torun successfully and to be free of unrealistic oscillations. Inthat regard, a 2e-5 sec simulation time step was found to bethe best for a typical automotive A/C model, and with that,the execution speed is on the order of 10 times that of real

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time speed on a 64 bit Windows computer. It is certainlydesirable to improve the execution speed, and current effortsare aimed to create versions of the model that trade some ofthe transient simulation accuracy for a much improvedexecution speed.

Execution speed is also dependent on the number ofsegments in the heat exchanger flat tubes or plates. In thecurrent model, 18 segments for the condenser flat tubes and10 segments for the evaporator plates were used. Fewersegments increase simulation speed due to both feweroperations per time step and the possibility of using largertime step, but at a cost of reduced accuracy.

Another measure of performance is how well theconservative variables are preserved. This is importantbecause when highly transient processes for long simulationtimes are modeled a loss of refrigerant mass due to numericalinaccuracies may be experienced leading to unacceptableerrors. The finite volume formulation implemented in themodel preserves mass and energy of the refrigerant with highaccuracy. Evaluating mass and energy conservation on thesystem level is relatively easily done and it provides a goodcheck on the error free implementation of the governingequations. Momentum is lost as refrigerant enters the 0-Dvolumes from the 1-D pipes, so it is not usable in this regardon the system level.

To demonstrate the conservativeness of the model, dataobtained with the mechanical drive compressor version forthe 600 second long SC03 cycle were used (see the ‘Results’section). To check on conservation of mass, the totalrefrigerant mass in the system was summed at the beginningand at the end, and the difference was less than 0.001 %. Asimilar check on the conservation of energy was also carriedout. According to the First Law of Thermodynamics, the finaltotal energy in the refrigerant must equal the initial totalenergy in the refrigerant plus the total energy transferred tothe refrigerant via heat transfer and by the compressor work.The deviation, once again, turned out to be less than 0.001%.

VERIFICATION AND RESULTSSystem Level Verification

Measured data for calibration and verification are not easyto obtain as they are guarded by the componentmanufacturers. However, some limited calibration andverification of the model with the use of steady stateperformance data on an actual light-duty A/C system havebeen carried out. Because the heat exchanger air inflowparameters were known and they were constant in time, thecabin model was essentially deactivated.

The data set used for verification included 22 steady-stateoperating points. The bench data included pressures andtemperatures along the entire refrigerant circuit, properties ofthe upstream and downstream air streams on the heatexchangers, and the compressor speed and mass flow ratedata. The evaporator superheat was measured, and the TXVmodel was set up for this nominal superheat. The internal

details of the TXV used in the tests were not known, but didnot matter for the calibration of the model for the rest of thesystem.

From the measured compressor mass flow rate and fromthe inlet and outlet refrigerant thermodynamic properties, thevolumetric and isentropic efficiencies of the compressor werecalculated as a function of compressor RPM and pressureratio. When the simulation was carried out, the compressorRPM was set to the measured one. For a properly verified andcalibrated model, the compressor performance had toconverge to the measured pressure ratio and mass flow rate.Showing a good match between measured and predictedrefrigerant mass flow rates over a significant range ofoperating points also verifies that it is acceptable to usevolumetric and the isentropic efficiencies as functions ofRPM and pressure ratio.

Uncertainty analysis for the measurements was notavailable; however, data on reproducibility provided ameasure of the integrity of the data. The relative deviation ofresults between an original and a repeated test, averaged forsix operating points, were 1.0%, 3.2% and 1.1%, forevaporator heat transfer, compressor power and refrigerantmass flow rate, respectively. A source of inaccuracy in thevalidation process was the fact that lube oil was present in themeasured system but was not accounted for in the simulation.

Since the actual geometry of the transport pipesconnecting the A/C components were not available, themodel version used for the verification did not include thesimulation blocks for the transport pipes. According to themeasured data, refrigerant property changes over mosttransport pipes could be neglected except for the pipeconnecting the evaporator outlet and the compressor inlet.The effect of the losses in this pipe on the systemperformance was simply represented by a pressure/enthalpychange simulation block between the evaporator refrigerantoutlet and the compressor inlet.

With these constraints, all 22 measurement points weresimulated, and some calibration was done on the heat transfercorrelation coefficients. Note that the need for calibration isespecially justified given that the evaporator plates utilized“dimples” to enhance the heat transfer rate and on the air sidethe presence of condensation most likely significantly alteredthe heat transfer rates compared to the Chang correlation. InFigs. 6.a and 6.b, the thermodynamic cycles for measurementpoints 4 and 6, respectively, are shown on the pressure-enthalpy space. These two points are representative of the full22-point series in terms of the quality of the match, and thematch between the simulation and the measurement is seen asquite good.

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Fig. 6a. Thermodynamic cycle for Test Point 4

Fig. 6b. Thermodynamic cycle for Test Point 6

Component Level VerificationFour pieces of component data were also derived from

each of the full cycle results. These include the refrigerantflow rate (constant through the system for the steady statepoints), the refrigerant-side heat transfer rate on thecondenser, the refrigerant-side heat transfer rate on theevaporator, and the evaporator-out air temperature. Themeasured and simulated data for these four properties areincluded in Figs. 7a, 7b, 7c and 7d, respectively.

Fig. 7a. Predicted and measured compressor mass flowrate

Fig. 7b. Predicted and measured condenser heatexchange rate

Fig. 7c. Predicted and measured evaporator heatexchange rate

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Fig. 7d. Predicted and measured evaporator air-outtemperature

Figs. 7a, 7b, 7c and 7d show that a good match betweenthe measured and the simulated data was achieved. Theaverage errors were 3.1%, 1.4%, 2.2% and 0.7°C,respectively.

ResultsThe SC03 cycle was simulated with both the mechanical

and the electric drive compressor versions of the model. Themodels were set up for the same system geometry and initialconditions. The results for the mechanical drive compressorare shown in Figs. 8a, b, c and d, and the results for theelectric drive compressor are shown in Figs. 9 a, b, c and d.

Fig. 8a. Compressor and drive speed, mechanical drive,SC03 cycle

Fig. 8b. Compressor power and heat transfer ratesmechanical drive, SC03 cycle

Fig. 8c. Evaporator air-out temperature with compressorswitch limits and control signal, mechanical drive, SC03

cycle

Fig. 8d. Cabin temperatures with compressor switchlimits and control signal, mechanical drive, SC03 cycle

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Note that for the mechanical drive compressor, the

compressor speed is either a pulley ratio times the drivespeed, when the compressor is on, or zero, when thecompressor is off. In Fig. 8c, the “Compr. On Level” is thetemperature that the evaporator exit air temperature has topass in the upward direction for a “compressor on” trigger,and the “Compr. Off Level” is a temperature slightly lowerthat the evaporator exit air temperature has to pass in thedownward direction for a compressor off trigger. In Fig. 8d,the “Compr. On Level” is a temperature that the cabin airtemperature has to pass in the upward direction for a“compressor on” trigger and the “Compr. Off Level” is atemperature that the cabin air temperature has to pass in thedownward direction for a “compressor off” trigger.

Results for the SC03 cycle with the electric drivecompressor A/C model (shown in Figs. 9a,9b,9c,9d) arepresented slightly differently as the controls are different.Note the lack of compressor cycling, which is achieved by acompressor speed that is independent of the engine speed.The evaporator wall temperature target was set at 3°C, andthe minimum for this temperature turned out to be 1.7°C. Thesmooth compressor speed trace allows for significantlyreduced transient spikes in most variables compared to themechanical drive compressor A/C model. For a differentproblem setup in which the target cabin temperature could beachieved with much lower average evaporator load,compressor cycling would be taking place as the compressorspeed would be driven down to below the minimum allowedspeed by the controller.

Fig. 9a. Vehicle velocity and scaled compressor speed.electric drive, SC03 cycle

Fig. 9b. Compressor shaft power and heat transfer rates,electric drive, SC03 cycle

Fig. 9c. Evaporator temperatures, electric drive, SC03cycle

Fig. 9d. Ambient and cabin temperatures, electric drive,SC03 cycle

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CONCLUSIONSA new automotive A/C system simulation tool developed

on the MATLAB/Simulink platform has been described. Themodel consists of a detailed cooling circuit model and arelatively simple cabin model. The governing equations forthe key system simulation blocks have been provided. Afinite volume formulation of the governing equations wasused on the refrigerant side, which provided a very accuratepreservation of refrigerant mass and a very accurate energybalance. The model can handle the fast transients that occurin an automotive A/C system.

Comparison of simulated data with test data for a set of 22steady state test points shows good agreement betweensimulation and measurement. For the refrigerant mass flowrate, the evaporator load, the condenser load, and theevaporator-out air temperature, the average errors were 3.1%,1.4%, 2.2% and 0.7°C, respectively. Two main versions ofthe model exist at this time, one version with a mechanicaldrive compressor and the other with an electric drivecompressor model. The main difference between the twoversions is the method of electronic controls, and someresults for both versions have been presented for the SC03cycle. This model is well suited for co-simulation withvehicle system analysis software and for development of A/Csystem controls for optimized system performance. Themodel is also expected to be a useful tool for designingautomotive A/C systems, although such use has not beendemonstrated yet.

As a final note, the U.S. Environmental ProtectionAgency and the National Highway Traffic SafetyAdministration have recently published greenhouse gas(GHG) emission and fuel consumption regulations for 2012 -2016 and for 2017 - 2025 [16, 17]. These regulations includethe acknowledgement that A/C fuel consumption contributessignificantly to overall vehicle GHG emissions. In an attemptto reduce this amount, a credit scheme is being implementedso that auto makers that employ highly efficient A/Ccomponents are awarded GHG credits. While not an officialtool, the model presented in this paper can be useful forevaluating the reduction in GHG emissions over any drivecycle that results from using more efficient air conditioningcomponents. In this way the model can both aid regulatorsdefine credit amounts and assist car manufacturers indeciding among competing technologies.

REFERENCES1. Rugh, J. P., Hoveland, V., and Andersen, S. O. “Significant Fuel

Savings and Emission Reductions by Improving Vehicle AirConditioning,” Earth Technologies Forum/Mobile Air ConditioningSummit, 2004.

2. Umezu, K., and Noyama, H., “Air-Conditioning System for ElectricVehicles (i-MiEV),” SAE Automotive Alternate Refrigerant SystemsSymposium, 2010.

3. National Renewable Energy Laboratory, Vehicle Technologies Program2007 Annual Report, pp. 145.

4. Stodolsky, F., Gaines, L., and Vyas, A. Analysis of Technology Optionsto Reduce the Fuel Consumption of Idling Trucks. Argonne NationalLaboratory, ANL/ESD-43, June 2000

5. Computer Software “Autonomie”, www.autonomie.org

6. Hemami, T. L., “Development of a Transient System Model of MobileAir-Conditioning Systems,” ACRC Technical Report - 143, September1998.

7. Cullimore, B. A., and Hendricks, T. J., “Design and TransientSimulation of Vehicle Air Conditioning Systems,” VTMS 52001-01-1692

8. Anand, G., Mahajan, M., Jain, N., Maniam, B. et al., “e-Thermal:Automobile Air-Conditioning Module,” SAE Technical Paper2004-01-1509, 2004, doi:10.4271/2004-01-1509.

9. Streeter, V.L., and Wylie, E.B., “Fluid Mechanics” 7th edition,McGraw-Hill, 1979.

10. Incropera, F., P., and DeWitt, D.P., “Fundamentals of Heat and MassTransfer,” 2nd edition, 1985, John Wiley and Sons, Inc.

11. Chen, J.C., “Correlation for Boiling Heat Transfer to Saturated Fluids inConvective Flow,” I&EC Process Design and Development, Vol. 5. No.3 July 1966 pp.322 - 329.

12. Morales-Ruiz, S., Rigola, J., Perez-Segarra, C.D., and Garcia-Valladeres, O., “Numerical Analysis of Two-Phase Flow in Condensersand Evaporators with Special Emphasis on Single-Phase/Two-PhaseTransition Zones,” Applied Thermal Engineering, 2009 Volume 29, pp.1032 - 1042.

13. Chang, Y., and Wang, C., “A Generalized Heat Transfer Correlation forLouver Fin Geometry,” Int. J. Heat and Mass Transfer, vol. 40, No. 3,pp. 533-544, 1997.

14. Singh, G.M., Hrnjak, P.S., and Bullard, C.W., “Flow of Refrigerant134a Through Orifice Tubes,” HVAC&R Research, Vol. 7, No.3, pp.245-262, July 2001.

15. Cengel, Y.A., and Boles, M.A., “Thermodynamics - An EngineeringApproach,” McGraw-Hill, 1994.

16. Federal Register, May 7, 2010.17. Federal Register, August 28, 2012.

CONTACT INFORMATIONTibor [email protected]

Lawrence [email protected]

Jason [email protected]

ACKNOWLEDGMENTSThe authors would like to thank John Rugh and Jason

Lustbader of NREL for their contribution to this project.The authors would also like to thank Lee Slezak and

David Anderson, Technology Managers for the U.S.Department of Energy's Advanced Vehicle TechnologyAnalysis and Evaluation for sponsoring this work.

DEFINITIONS/ABBREVIATIONSA/C - Air ConditioningEV - Electric VehicleOEM - Original Equipment ManufacturerNREL - National Renewable Energy Laboratory0-D - Zero Dimensional1-D - One-DimensionalTXV - Thermostatic Expansion ValveRPM - Revolution per minuteGHG - Green House Gases

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